The first thing to note is the 3 resistors between pin 8 and 1 (all 5k)
Using the voltage division theorem you can calculate that the top resistor will drop !/3 rd of the supply - there will be 2/3 of the supply to ground.

The bottom resistor will drop 1/3 rd of the supply to ground

Two comparitors are connected to this resistor network

The top comparitor inputs connect pin 6 (THRESHOLD) and the top resistor of the network. (point A)

The bottom comparitor inputs connect pin 2  (TRIGGER) and the bottom resistor of the network. (point B)

Once pin 6 (THRESHOLD) voltage tries to rise more than  2/3 of the supply (rising voltage caused by capacitor C charging via resistor R1 and R2) this comparitor will change state 

The flip flop will trigger in the 555 timer which will result in the transistor connected to pin 7 (the discharge pin) turning on.

When this fires the external capacitor will discharge until the voltage reaches 1/3 rd of the supply.

At this point the circuit will automatically trigger itself because the bottom comparitor will be triggered by the falling voltage.

The capacitor will now start to charge and the sequence will repeat itself.

Remember - Astable pins 2 and 6 are connected together to supply via a resistor

In the monstable the output is permanently being pulled low

The trigger that is applied to the trigger pin (pin 2) also pulls the pin towards ground.

This makes the lower comparitor change state triggering flip flop 

This turns off the transistor that is permanantley on  in the monostable configuration

This allows the capacitor to charge.

Once this reaches 2/3 rds the supply voltage then the top comparitor will trigger, the discharge transistor will turn on once again discharging the capacitor.

It will remain in this state until the the trigger switch is pressed